To map the frequency-time domain 2-D sequence \( \mathbf {X} \)  to a time domain signal transmitted over the wireless channel, we apply the Heisenberg transform [1]}, [2]}, which entails an \(N\) -point IFFT together with a transmit pulse-shaping waveform \(g_{\rm {tx}}(t)\)  (which is time limited to \(\left[0, \, T \right]\) ). The time domain signal corresponding to the \( {m^{\rm {th} } } \)  symbol after the Heisenberg transform can be written as
\(s_m(t) = \frac{1}{\sqrt{N}} \sum _{n = 0}^{N-1}  x_{n,m} \, e^{j 2 \pi n  \Delta f t} g_{\rm {tx}}(t) \,, ~ 0 \le t \le T ~,\) 
